Density Measures
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908912757768192 |
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| author | Schönherr, Moritz Schuricht, Friedemann |
| author_facet | Schönherr, Moritz Schuricht, Friedemann |
| contents | The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied to the precise representative of general integrable functions and then they are specialized to functions of bounded variation. Moreover, a new representation of the generalized gradients in the sense of Clarke is given for the finite dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Density Measures Schönherr, Moritz Schuricht, Friedemann Analysis of PDEs Optimization and Control 28A12, 46E35, 26B30, 49J52 The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied to the precise representative of general integrable functions and then they are specialized to functions of bounded variation. Moreover, a new representation of the generalized gradients in the sense of Clarke is given for the finite dimensional case. |
| title | Density Measures |
| topic | Analysis of PDEs Optimization and Control 28A12, 46E35, 26B30, 49J52 |
| url | https://arxiv.org/abs/2603.24163 |